How do I get my offset models to be at 0, 0, 0?
Switch to 'Edit mode' (Tab key).
Press A key. This will select all the verts in the model.
In Orthographic view (Numbad 5) move the selected group of verts over the orange dot (the origin).
Repeat this step in orthographic view for X, Y and Z.
Back to Object mode, select the model, choose Object> Apply> All Transforms. This just resets any scale or transform issues.